How efficient can an English Language Teacher (Non-native) be outside of his own country; Teaching in the Middle East for Example?

I think, if you mean secondary schools, you should care for making them understand what you are saying; talk slowly and clearly.2) Make a sort of friendship with them.3) learn some Arabic terminology related to the students, class and use them occasionally; it help them relax.4) Reward the good ones.

Before taking into considerations what course anyone intends to teach, the most important thing to keep in mind is the question: Who is a good teacher? Speaking out of personal knowledge and observation, a good teacher is the person who can transform knowledge into information that can be processed by the students minds, regardless of the topic, the quantity of the the knowledge this teacher has is critical but not most vital; whilst the quality of the student should always remain irrelevant, a good teacher must be always determined to "FIND" the best way to deliver the course's material.
Bottom line is: A non-native Chinese language teacher can be efficient teaching outside his country if he's good at teaching in general.

I think if you are a good ELT, it does not matter where you are.
As a speaker of English you should be familiar with many cultures and be tolerant and accept differences.
This is what I focus on, besides teaching the language I also teach my students how to accept people different from them.
A non-native teacher knows the ups and downs of learning English and has mastered at least one foreign language.
Most native speakers do not speak any other languages so they have very basic experiences in learning a new language.
Efficiency greatly depends on the relationship between the teacher and the students.
Of course I have a lot more to say about this topic but as an intro to your question this should do.
I would be happy to answer question relating to this topic.

Please define native and non native speaker of English ?These are nonsense terms !!!

Non native teachers understand the learning problems of their students more easily and have empathic approach towards them. They do understand that the students might face basic difficulties while learning English.